Construction Of A Rich Word Containing Given Two Factors

A finite word $w$ with $\vert w\vert=n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is attained, the word $w$ is called \emph{rich}. Let \Factor(w) be the set of factors of the word $w$. It is known that there are pairs of rich words that cannot be factors of a common rich word. However it is an open question how to decide for a given pair of rich words $u,v$ if there is a rich word $w$ such that \{u,v\}\subseteq \Factor(w). We present a response to this open question:\\ If $w_1, w_2,w$ are rich words, $m=\max{\{\vert w_1\vert,\vert w_2\vert\}}$, and \{w_1,w_2\}\subseteq \Factor(w) then there exists also a rich word $\bar w$ such that \{w_1,w_2\}\subseteq \Factor(\bar w) and $\vert \bar w\vert\leq m2^{k(m)+2}$, where $k(m)=(q+1)m^2(4q^{10}m)^{\log_2{m}}$ and $q$ is the size of the alphabet. Hence it is enough to check all rich words of length equal or lower to $m2^{k(m)+2}$ in order to decide if there is a rich word containing factors $w_1,w_2$

Proof of Brlek-Reutenauer conjecture

Brlek and Reutenauer conjectured that any infinite word u with language closed under reversal satisfies the equality 2D(u) = \sum_{n=0}^{\infty}T_u(n) in which D(u) denotes the defect of u and T_u(n) denotes C_u(n+1)-C_u(n) +2 - P_U(n+1) - P_u(n), where C_u and P_u are the factor and palindromic complexity of u, respectively. This conjecture was verified for periodic words by Brlek and Reutenauer themselves. Using their results for periodic words, we have recently proved the conjecture for uniformly recurrent words. In the present article we prove the conjecture in its general version by a new method without exploiting the result for periodic words.Comment: 9 page

A study of environmental characterization of conventional and advanced aluminum alloys for selection and design. Phase 2: The breaking load test method

A technique is demonstrated for accelerated stress corrosion testing of high strength aluminum alloys. The method offers better precision and shorter exposure times than traditional pass fail procedures. The approach uses data from tension tests performed on replicate groups of smooth specimens after various lengths of exposure to static stress. The breaking strength measures degradation in the test specimen load carrying ability due to the environmental attack. Analysis of breaking load data by extreme value statistics enables the calculation of survival probabilities and a statistically defined threshold stress applicable to the specific test conditions. A fracture mechanics model is given which quantifies depth of attack in the stress corroded specimen by an effective flaw size calculated from the breaking stress and the material strength and fracture toughness properties. Comparisons are made with experimental results from three tempers of 7075 alloy plate tested by the breaking load method and by traditional tests of statistically loaded smooth tension bars and conventional precracked specimens

On Words with the Zero Palindromic Defect

We study the set of finite words with zero palindromic defect, i.e., words rich in palindromes. This set is factorial, but not recurrent. We focus on description of pairs of rich words which cannot occur simultaneously as factors of a longer rich word

Original approach for thrombolytic therapy in patients with Ilio-femoral deep vein thrombosis: 2 years follow-up

Objective: The aim of the study was to discuss the results of catheter-directed thrombolysis and complementary procedures to treat acute iliofemoral deep vein thrombosis (DVT) evaluating the safety and effectivness of an easy access such as the Great Saphenous Vein. Methods and materials: A total of 22 consecutive patients with iliofemoral thrombosis and two patients with femoro-popliteal thrombosis on recent onset diagnosed with Ultrasound Doppler and contrast venography underwent intrathrombus drip infusion of urokinase while intravenous heparin was continued using saphenical access. Residual venous stenosis were treated in six patients by percutaneous balloon Angioplasty and stenting. All patients underwent routine venous duplex imaging at 30 days, 3 months, 6 months and every 6 months thereafter. Results: Complete patency of thrombosed veins was restored in 22 patients (91 %) with prompt symptomatic relief. There were no major complications in the immediate outcomes. At follow-up, two patients reported a persistant slim iliac vein stenosis, two patients had post-thrombotic syndrome, and two patients showed Deep Vein Reflux. Conclusion: Local thrombolysis using saphenical access was a safe and effective approach for the treatment of acute iliofemoral deep vein thrombosis. It seems to be a valid, easy and safe alternative, reducing the risks of haematoma and venous lesions, which can be observed when using femoral, popliteal, and trans-jugular access

Growth and dissection of a fold and thrust belt: the geological record of the High Agri Valley, Italy

We present a 130 km2 wide geological map for the NE side of the fault-bounded High Agri Valley Southern Italy, that formed in the Quaternary in response to extensional tectonics dissecting the folds and thrusts of the Lucanian Apennine. To prepare the map, at 1:25,000 scale, we integrated information obtained through field surveys and the review of pre-existing geological data. Our work describes a number of significant map-scale structures, which can be related to well-constrained tectonic episodes. The new geological map provides important constraints that can be used to distinguish ancient structures from those that were active during the Quaternary, allowing a more detailed reconstruction of the processes that operate during the development of a post-orogenic trough. We expect that the new map will be used for different types of geological investigations, including studies of inversion tectonics, active tectonics, geosite mapping, 3D modelling of geological structures. © 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of Journal of Maps

A Novel Gaussian Extrapolation Approach for 2D Gel Electrophoresis Saturated Protein Spots

Analysis of images obtained from two-dimensional gel electrophoresis (2D-GE) is a topic of utmost importance in bioinformatics research, since commercial and academic software available currently has proven to be neither completely effective nor fully automatic, often requiring manual revision and refinement of computer generated matches. In this work, we present an effective technique for the detection and the reconstruction of over-saturated protein spots. Firstly, the algorithm reveals overexposed areas, where spots may be truncated, and plateau regions caused by smeared and overlapping spots. Next, it reconstructs the correct distribution of pixel values in these overexposed areas and plateau regions, using a two-dimensional least-squares fitting based on a generalized Gaussian distribution. Pixel correction in saturated and smeared spots allows more accurate quantification, providing more reliable image analysis results. The method is validated for processing highly exposed 2D-GE images, comparing reconstructed spots with the corresponding non-saturated image, demonstrating that the algorithm enables correct spot quantification

A novel Gaussian fitting approach for 2D gel electrophoresis saturated protein spots

Analysis of 2D-GE images is a hot topic in bioinformatics research, since currently available commercial and academic software has proven to be not really effective and not completely automatic, often requiring manual revision of spots detection and refinement of computer generated matches. In this work, we present an effective technique for the detection and the reconstruction of over-saturated protein spots. Firstly, it reveals overexposed areas where spots may be truncated, and plateau regions caused by smeared and overlapped spots. As next, the correct distribution of pixel values in the overexposed areas and plateau regions is recovered by a two-dimensional fitting based on a generalized Gaussian distribution approximating the spots volume. Pixel correction according to the generalized Gaussian curve in saturated and smeared spots allows more accurate quantifications, providing more reliable image analysis results. As validation, we process highly exposed 2D-GE image, containing saturate spots, with respect to the corresponding non-saturated image, confirming that the method can effectively fix the saturated spots and enable correct spots quantification

EFFECTS OF RESVERATROL ON VITRIFIED PORCINE OOCYTES

Vitrified MII porcine oocytes are characterized by reduced developmental competence, associated with the activation of the apoptotic pathway. Resveratrol (R), a polyphenolic compound present in several vegetal sources, has been reported to exert, among all its other biological effects, an antiapoptotic one. The aim of this study was to determine the effects of R (2\u2009\ub5M) on the apoptotic status of porcine oocytes vitrified by Cryotop method, evaluating phosphatidylserine (PS) exteriorization and caspases activation. R was added during IVM (A); 2\u2009h postwarming incubation (B); vitrification/warming and 2\u2009h postwarming incubation (C); all previous phases (D). Data on PS exteriorization showed, in each treated group, a significantly higher (P<0.05) percentage of live nonapoptotic oocytes as compared with CTR; moreover, the percentage of live apoptotic oocytes was significantly (P<0.05) lower in all R-treated groups relative to CTR. The results on caspase activation showed a tendency to an increase of viable oocytes with inactive caspases in B, C, and D, while a significant (P<0.05) increase in A compared to CTR was recorded. These data demonstrate that R supplementation in various phases of IVM and vitrification/warming procedure can modulate the apoptotic process, improving the resistance of porcine oocytes to cryopreservation-induced damage